Fountain codes are typical channel erasure error correction codes that can achieve a channel capacity by using encoding symbols equal to or slightly larger than the number of messages in an algorithm of low complexity. The fountain code is more effective in a broadcasting system where a plurality of receivers exist because it is determined whether data can be restored or not based on only the number of received symbols. For example, a Luby Transform (LT) code using a Robust Soliton Distribution (RSD), a raptor code included in the 3rd Generation Partnership Project (3GPP) Multimedia Broadcast and Multicast System (MBMS) standard, etc. are known as fountain codes.
When an environment that ensures reception of a plurality of symbols is not guaranteed, the receiver succeeds in restoring the symbols with very low probability. Research on a fountain code design for maximizing a symbol restoration probability when the number of received encoding symbols is smaller than the number of messages is ongoing. Furthermore, research on a code design for maximizing an average symbol restoration probability when the number of received encoding symbols is a random variable is also ongoing.
It is not always guaranteed that the number of received encoding symbols is larger than the number of messages. Accordingly, there is a need for a fountain code design when the number of received encoding symbols is smaller than the number of messages. However, existing research limits a channel erasure rate to a fixed constant value and thus an optimal code design cannot be achieved when a broadcasting service requiring a plurality of receivers is provided. Accordingly, there is a need to provide a new fountain code and a degree distribution considering a more accurate channel erasure model than a fountain code defined on the premise of a fixed channel erasure rate in a wireless communication system.
The above information is presented as background information only to assist with an understanding of the present disclosure. No determination has been made, and no assertion is made, as to whether any of the above might be applicable as prior art with regard to the present disclosure.